Theory of Computing

Module overview

This module aims to provide a broad and stimulating introduction to the theory of computing.

Aims and Objectives

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

Use polynomial-time reduction to reason about the complexity class of a problem
Use the reduction technique to show that a problem is undecidable
Analyse the complexity of a given algorithm or problem
Ascertain and prove whether or not a given language is regular
Ascertain and prove whether or not a given language is context-free

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

The diagonalisation proof technique
The relationship between the regular, context-free and recursively enumerable classes of languages, and the state-machines that accept them
The nature and examples of undecidable problems
The complexity of algorithms and problems, and key complexity classes

Learning and Teaching

Teaching and learning methods

The content of this module is delivered through lectures, the module website, directed reading, pre-recorded materials and tutorials. Students work on their understanding through a combination of independent study, preparation for timetabled activities, tutorials, and problem classes, along with formative assessments in the form of problem sheets.

Study time
Type	Hours
Follow-up work	18
Lecture	36
Wider reading or practice	50
Preparation for scheduled sessions	6
Revision	18
Tutorial	12
Completion of assessment task	10
Total study time	150

Resources & Reading list

Textbooks

J. Hein (2002). Discrete Structures, Logic and Computability. Jones and Bartlett.

A.J.G. Hey (1996). Feynman Lectures on Computation. Addison Wesley.

J. Barwise and J. Etchemendy (1993). Turing's World. Stanford.

D.C. Kozen (1999). Automata and Computability. Springer.

M. Sipser (1997). Introduction to the Theory of Computation. PWS.

D. Cohen (1996). Introduction to Computer Theory. Wiley.

J. Gruska (1996). Foundations of Computing. Thomson.

D. Harel (1992). Algorithmics: The Spirit of Computing. Addison Wesley.

N.D. Jones (1999). Computability and Complexity. MIT Press.

A.K. Dewdney (2001). The (new) Turing Omnibus. Henry Holt.

Assessment

Assessment strategy

This module is assessed by a combination of problem sheets and a final assessment in the form of a written examination.

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Examination	100%